mathsurgery - Mental calculations and checking year 9

All
• Identify the mathematical features of a context or problem
• Understand and use the rules of arithmetic and inverse operations in the context of integers and fractions
• Use the order of operations, including brackets, with more complex calculations
• Strengthen and extend mental methods of calculation, working with decimals, fractions, percentages, squares and square roots, and cubes and cube roots; solve problems mentally
• Recall equivalent fractions, decimals and percentages; use known facts to derive unknown facts, including products involving numbers such as 0.7 and 6, and 0.03 and 8
• Make and justify estimates and approximations of calculations
• Select from a range of checking methods, including estimating in context and using inverse operations

Most
• Break down substantial tasks to make them more manageable
• Estimate, approximate and check working
• Understand the effects of multiplying and dividing by numbers between 0 and 1; consolidate use of the rules of arithmetic and inverse operations
• Understand the order of precedence of operations, including powers
• Use known facts to derive unknown facts; extend mental methods of calculation, working with decimals, fractions, percentages, factors, powers and roots; solve problems mentally
• Check results using appropriate methods

Some
• Explain the features selected and justify the choice of representation in relation to the context
• Round to a given number of significant figures; use significant figures to approximate answers when multiplying or dividing large numbers
• Make and justify estimates and approximations of calculations by rounding numbers to one significant figure and multiplying or dividing mentally
• Recognise and use reciprocals; understand ‘reciprocal’ as a multiplicative inverse; know that any number multiplied by its reciprocal is 1, and that zero has no reciprocal because division by zero is not defined

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Mental calculations and checking year 9